discussion in Chapter 4). In fact, even if PI said that all Green Party members are vegetarians, the inference would be mistaken. For suppose that only one out of every 101 people (in the UK, for example) is a member of the Green Party. If the remaining (non-Green) population is 10 per cent vegetarian, then, since every Green is vegetarian, eleven out of every 101 people are vegetarian. But only one of those eleven is a Green. Thus ten out of every 101 people are non-Green vegetarians, and the non-Green vegetarians outnumber the Green vegetarians by ten to one! So if you meet a vegetarian such as Alistair, then, unless you had other reasons to think he is a Green, the reasonable expectation would be that he is not a Green. Summing up, then, the premises do not give you a good reason to think that Alistair is a Green.
The problem is that the premises seem to tell us that if someone is a vegetarian, then, probably, they are a Green. But they do not. Similarly: All plumbers own pipe wrenches, and few non-plumbers own them; but these facts do not entitle us to say that if someone owns a pipe wrench, then probably, they are a plumber. As a matter of fact, many DIYers own pipe wrenches. So the number of non-plumbers owning pipe wrenches may well outnumber the plumbers.
The conclusion of an inductively forceful argument may serve as a premise for a further argument, which may itself be deductively valid, inductively forceful, or neither. However, if any sub-argument of an extended argument is not deductively valid, then the argument as a whole is not deductively valid. At most, it is inductively forceful. Here is a hybrid extended argument which illustrates the point:
P1) If Napoleon is not ill then the French will attack.
P2) Probably, Napoleon is not ill.
C1) (Probably) The French will attack.
P3) If the French attack, then the Prussians will be routed.
C2) (Probably) The Prussians will be routed.
If the first argument were valid, entitling us to assert CI categorically -that is, without the qualifier 'Probably' - then since the argument from CI and P2 to C2 is deductively valid, there would be no need to write
Logic: inductive force
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